The infimum of the empty set is defined as infinity (inf∅ = ∞) to ensure consistency in calculations involving subsets. If inf∅ were assigned a finite value, it would create contradictions with the infimum of sets containing elements. Similarly, the supremum of the empty set is defined as negative infinity (sup∅ = -∞) to maintain coherence in mathematical operations. This approach effectively removes the empty set from influencing the calculations of infimum and supremum. The definitions serve to streamline mathematical reasoning involving these concepts.
